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Physical review. B, Condensed matter

Electronic excitation spectra of the Emery model

Patrick Unger, Peter Fulde

Published Apr 1, 1993• 30 citations
Publisher

Abstract

We calculate the photoemission and inverse photoemission spectra of holes in copper-oxygen planes, the characteristic structural unit of high-temperature superconductors. The computations are based on the extended Hubbard or Emery model in the limit of infinitely strong Coulomb repulsion ${\mathit{U}}_{\mathit{d}}$ on copper sites. In order to evaluate the corresponding one-particle correlation functions the projection technique is applied, which is especially suitable for strongly correlated systems. Thereby the hole dynamics is restricted to a subspace of relevant operators, within which it can be treated exactly. In contrast to independent-particle approximations the excitation spectra show an energy gap at half-filling, which disappears when the system is doped with additional holes. Besides the insulator-to-metal transition the strong correlations lead also to a significant shift of spectral weight to states close to the Fermi energy when the hole concentration increases. Our results are in good agreement with the ones of exact diagonalization studies of the (${\mathrm{CuO}}_{2}$${)}_{4}$ cluster with periodic boundary conditions.

DOI
10.1103/physrevb.47.8947

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We calculate the photoemission and inverse photoemission spectra of holes in copper-oxygen planes, the characteristic structural unit of high-temperature superconductors. The computations are based on the extended Hubbard or Emery model in the limit of infinitely strong Coulomb repulsion Ud{\mathit{U}}_{\mathit{d}}Ud​ on copper sites. In order to evaluate the corresponding one-particle correlation functions the projection technique is applied, which is especially suitable for strongly correlated systems. Thereby the hole dynamics is restricted to a subspace of relevant operators, within which it can be treated exactly. In contrast to independent-particle approximations the excitation spectra show an energy gap at half-filling, which disappears when the system is doped with additional holes. Besides the insulator-to-metal transition the strong correlations lead also to a significant shift of spectral weight to states close to the Fermi energy when the hole concentration increases. Our results are in good agreement with the ones of exact diagonalization studies of the ({\mathrm{CuO}}_{2}$${)}_{4} cluster with periodic boundary conditions.
We calculate the single-particle excitation spectrum of holes in the Emery model thereby extending and improving previous calculations. The system is considered at half filling (nh{\mathit{n}}_{\mathit{h}}nh​=1, one hole per CuO2{\mathrm{CuO}}_{2}CuO2​ unit) and for hole doping, where the on-site hole-hole repulsions are kept finite. A paramagnetic form of the ground state is used. For the determination of the retarded Green's functions of copper and oxygen holes, the projection technique is applied solving the resulting equations of motions self-consistently. At half filling, the excitation spectrum exhibits a charge-transfer gap bounded by Zhang-Rice singlet states and the upper Hubbard band. Upon hole doping the flat singlet band crosses the Fermi level giving rise to a large Fermi surface at a hole concentration of nh{\mathit{n}}_{\mathit{h}}nh​=1.25. Moreover, spectral weight is shifted from the upper Hubbard band to the states near the Fermi energy. The calculated spectral densities, the singlet dispersion for the doped system, and the transfer of spectral weight are in good quantitative agreement with exact diagonalization results for 2\ifmmode\times\else\texttimes\fi{}2 CuO2{\mathrm{CuO}}_{2}CuO2​ cluster.
We consider a single copper oxide plane with infinite Hubbard U on the copper sites and direct oxygen-oxygen and copper-oxygen overlaps as a model for high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials. Using a slave-boson representation, we find a region of parameter space with a charge-transfer-type metal-insulator transition at zero doping, i.e, half-filling in a mean-field limit. Performing a 1/N expansion we calculate the photoemission and inverse-photoemission spectra near the transition for both the n-type and p-type high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials using the sudden approximation.
We present a theoretical description of the one-particle excitation spectra in strongly correlated systems with nonlocal interactions. Using exact diagonalization techniques, photoemission and inverse photoemission spectra of an extended Hubbard model with an intersite Coulomb interaction are calculated. The single-particle and many-body aspects are treated on an equal footing. The hopping and interaction parameters are adjusted to simulate various Hubbard and charge-transfer systems. In contrast to normal expectations, the intersite interaction is found to suppress the spectral features driven by the on-site interaction, leading to a narrowing in the overall spectral distribution. It also produces qualitatively new behavior in the spin polarization of the spectra and in the doping dependence of the low-energy spectral weight. The degree of sensitivity of the spectra to the single-particle and interaction parameters is systematically investigated. General implications of the calculated results for strongly correlated systems are discussed.
Calculations of the single-particle spectral function for the two-band Hubbard model as a function of doping and nearest-neighbor Coulomb repulsion are performed on finite-size clusters. It is shown that for hole doping the effect of the nearest-neighbor Coulomb repulsion leads to the effective pinning of the Fermi energy, and to the creation of new states in the charge-transfer gap. For electron doping, however, the model behaves as a one-band Hubbard model with the Fermi energy moving into the conduction band. The results of this calculation are in qualitative agreement with some of the spectroscopic studies of the electronic structure at the Fermi energy of the high-temperature cuprate superconductors.
The three-band model relevant to high-temperature copper-oxide superconductors is solved using single-site dynamical mean field theory and a tight-binding parametrization of the copper and oxygen bands. For a band filling of one hole per unit cell the metal/charge-transfer-insulator phase diagram is determined. The electron spectral function, optical conductivity, and quasiparticle mass enhancement are computed as functions of electron and hole doping for parameters such that at one hole per cell the paramagnetic phase is insulating and for parameters such that at one hole per unit cell the paramagnetic phase is metallic. The optical conductivity is computed using the Peierls phase approximation for the optical matrix elements. The calculation includes the physics of ``Zhang-Rice singlets.'' The effects of antiferromagnetism on the magnitude of the gap and the relation between correlation strength and doping-induced changes in state density are determined. Three-band and one-band models are compared. The two models are found to yield quantitatively consistent results for all energies less than about 4 eV including energies in the vicinity of the charge-transfer gap. Parameters on the insulating side of the metal/charge-transfer insulator phase boundary lead to gaps which are too large and near-gap conductivities which are too small relative to data. The results place the cuprates clearly in the intermediate correlation regime, on the paramagnetic metal side of the metal/charge-transfer insulator phase boundary.
Methods are described which can be used for an analytical description of the strong electron correlations in the planes of the Cu–O based high-Tc superconducting materials. One is a projection technique which is applied in order to calculate the photoelectron and inverse photoelectron spectra for the cases of half filling and hole doping of the Cu–O planes. Good agreement with the results of exact diagonalization of (CuO2)4 clusters is obtained, proving the usefulness of the method. Another one is the concept of string states which can be applied to study the t–J model. Also in this case a number of numerical findings can be reproduced and improved by this analytic method.